| 1 | //===-- Single-precision general exp/log functions ------------------------===// |
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| 2 | // |
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| 3 | // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
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| 4 | // See https://llvm.org/LICENSE.txt for license information. |
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| 5 | // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
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| 6 | // |
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| 7 | //===----------------------------------------------------------------------===// |
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| 8 | |
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| 9 | #include "inv_trigf_utils.h" |
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| 10 | |
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| 11 | namespace LIBC_NAMESPACE { |
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| 12 | |
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| 13 | // Polynomial approximation for 0 <= x <= 1: |
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| 14 | // atan(x) ~ atan((i/16) + (x - (i/16)) * Q(x - i/16) |
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| 15 | // = P(x - i/16) |
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| 16 | // Generated by Sollya with: |
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| 17 | // > for i from 1 to 16 do { |
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| 18 | // mid_point = i/16; |
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| 19 | // P = fpminimax(atan(mid_point + x), 8, [|D...|], [-1/32, 1/32]); |
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| 20 | // print("{", coeff(P, 0), ",", coeff(P, 1), ",", coeff(P, 2), ",", |
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| 21 | // coeff(P, 3), ",", coeff(P, 4), ",", coeff(P, 5), ",", coeff(P, 6), |
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| 22 | // ",", coeff(P, 7), ",", coeff(P, 8), "},"); |
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| 23 | // }; |
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| 24 | // For i = 0, the polynomial is generated by: |
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| 25 | // > P = fpminimax(atan(x)/x, 7, [|1, D...|], [0, 1/32]); |
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| 26 | // > dirtyinfnorm((atan(x) - x*P)/x, [0, 1/32]); |
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| 27 | // 0x1.feb2fcdba66447ccbe28a1a0f935b51678a718fb1p-59 |
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| 28 | // Notice that degree-7 is good enough for atanf, but degree-8 helps reduce the |
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| 29 | // error bounds for atan2f's fast pass 16 times, and it does not affect the |
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| 30 | // performance of atanf much. |
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| 31 | double ATAN_COEFFS[17][9] = { |
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| 32 | {0.0, 1.0, 0x1.3f8d76d26d61bp-47, -0x1.5555555574cd8p-2, |
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| 33 | 0x1.0dde5d06878eap-29, 0x1.99997738acc77p-3, 0x1.2c43eac9797cap-16, |
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| 34 | -0x1.25fb020007dbdp-3, 0x1.c1b6c31d7b0aep-7}, |
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| 35 | {0x1.ff55bb72cfde9p-5, 0x1.fe01fe01fe007p-1, -0x1.fc05f809ed8dap-5, |
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| 36 | -0x1.4d69303afe04ep-2, 0x1.f61bc3e8349cp-5, 0x1.820839278756bp-3, |
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| 37 | -0x1.eda4de1c6bf3fp-5, -0x1.0514d42d64a63p-3, 0x1.db3746a442dcbp-5}, |
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| 38 | {0x1.fd5ba9aac2f6ep-4, 0x1.f81f81f81f813p-1, -0x1.f05e09d0dc378p-4, |
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| 39 | -0x1.368c3aa719215p-2, 0x1.d9b16b33ff9c9p-4, 0x1.40488f9c6262ap-3, |
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| 40 | -0x1.ba55933e62ea5p-4, -0x1.64c6a15cd9116p-4, 0x1.9273d5939a75ap-4}, |
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| 41 | {0x1.7b97b4bce5b02p-3, 0x1.ee9c7f8458e05p-1, -0x1.665c226d6961p-3, |
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| 42 | -0x1.1344bb7391703p-2, 0x1.42aca8b0081b9p-3, 0x1.c32d9381d7c03p-4, |
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| 43 | -0x1.13e970672e246p-3, -0x1.181ed934dd733p-5, 0x1.bad81ea190c08p-4}, |
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| 44 | {0x1.f5b75f92c80ddp-3, 0x1.e1e1e1e1e1e2cp-1, -0x1.c5894d10d363dp-3, |
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| 45 | -0x1.ce6de025f9f5ep-3, 0x1.78a3a07c8dd7fp-3, 0x1.dd5f5180f386ep-5, |
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| 46 | -0x1.1b1f513c4536bp-3, 0x1.0df852e58c43cp-6, 0x1.722e7a7e42505p-4}, |
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| 47 | {0x1.362773707ebccp-2, 0x1.d272ca3fc5b2ep-1, -0x1.0997e8aeca8fbp-2, |
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| 48 | -0x1.6cf6666e5e693p-3, 0x1.8dd1e907e88adp-3, 0x1.24849ac0caa5dp-7, |
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| 49 | -0x1.f496be486229dp-4, 0x1.b7d54b8e759ecp-5, 0x1.d39c0d39c3922p-5}, |
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| 50 | {0x1.6f61941e4def1p-2, 0x1.c0e070381c0f2p-1, -0x1.2726dd135d9eep-2, |
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| 51 | -0x1.09f37b39b70e4p-3, 0x1.85eacdaadd712p-3, -0x1.04d66340d5b9p-5, |
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| 52 | -0x1.8056b15a22b98p-4, 0x1.29baf494ad3ddp-4, 0x1.52d5881322a7ap-6}, |
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| 53 | {0x1.a64eec3cc23fdp-2, 0x1.adbe87f94906ap-1, -0x1.3b9d8eab55addp-2, |
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| 54 | -0x1.57c09646eb7p-4, 0x1.6795319e3b8dfp-3, -0x1.f2d89b5ef31bep-5, |
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| 55 | -0x1.f38aac26203cap-5, 0x1.3262802235e3fp-4, -0x1.2afd6b9a57d66p-7}, |
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| 56 | {0x1.dac670561bb4fp-2, 0x1.99999999999ap-1, -0x1.47ae147adff11p-2, |
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| 57 | -0x1.5d867c40188b7p-5, 0x1.3a92a2df85e7ap-3, -0x1.3ec457c46e851p-4, |
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| 58 | -0x1.ec1b9777e2e5bp-6, 0x1.0a542992a821ep-4, -0x1.ccffbe2f0d945p-6}, |
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| 59 | {0x1.0657e94db30dp-1, 0x1.84f00c2780615p-1, -0x1.4c62cb562defap-2, |
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| 60 | -0x1.e6495b3c14e03p-8, 0x1.063c2fa617bfcp-3, -0x1.58b782d9907aap-4, |
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| 61 | -0x1.41e6ff524b7fp-8, 0x1.937dfff3205a7p-5, -0x1.0fb1fd1c729dp-5}, |
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| 62 | {0x1.1e00babdefeb4p-1, 0x1.702e05c0b816ep-1, -0x1.4af2b78215fbep-2, |
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| 63 | 0x1.5d0b7e9f36997p-6, 0x1.a1247cb978debp-4, -0x1.519e1457734cap-4, |
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| 64 | 0x1.a755cf86b5bfbp-7, 0x1.096d174284564p-5, -0x1.081adf539ad58p-5}, |
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| 65 | {0x1.345f01cce37bbp-1, 0x1.5babcc647fa8ep-1, -0x1.449db09426a6dp-2, |
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| 66 | 0x1.655caac5896dap-5, 0x1.3bbbd22d05a61p-4, -0x1.34a2febee042fp-4, |
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| 67 | 0x1.84df9c8269e34p-6, 0x1.200e8176c899ap-6, -0x1.c00b23c3ce222p-6}, |
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| 68 | {0x1.4978fa3269ee1p-1, 0x1.47ae147ae1477p-1, -0x1.3a92a3055231ap-2, |
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| 69 | 0x1.ec21b515a4a2p-5, 0x1.c2f8b81f9a0d2p-5, -0x1.0ba9964125453p-4, |
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| 70 | 0x1.d7b5614777a05p-6, 0x1.971e91ed73595p-8, -0x1.3fc375a78dc74p-6}, |
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| 71 | {0x1.5d58987169b18p-1, 0x1.34679ace01343p-1, -0x1.2ddfb039136e5p-2, |
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| 72 | 0x1.2491307b9fb73p-4, 0x1.29c7e4886dc22p-5, -0x1.bca78bcca83ap-5, |
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| 73 | 0x1.e63efd7cbe1ddp-6, -0x1.8ea6c4f03b42dp-10, -0x1.9385b5c3a6997p-7}, |
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| 74 | {0x1.700a7c5784634p-1, 0x1.21fb78121fb76p-1, -0x1.1f6a8499e5d1ap-2, |
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| 75 | 0x1.41b15e5e29423p-4, 0x1.59bc953163345p-6, -0x1.63b54b13184ddp-5, |
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| 76 | 0x1.c9086666d213p-6, -0x1.90c3b4ad8d4bcp-8, -0x1.80f08ed9f6f57p-8}, |
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| 77 | {0x1.819d0b7158a4dp-1, 0x1.107fbbe01107ep-1, -0x1.0feeb4089670ep-2, |
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| 78 | 0x1.50e5afb93f5cbp-4, 0x1.2a7c2adffeffbp-7, -0x1.12bd29b4f1b43p-5, |
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| 79 | 0x1.93f71f0eb00eap-6, -0x1.10ece5ad30e28p-7, -0x1.db1a76bcd2b9cp-10}, |
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| 80 | {0x1.921fb54442d18p-1, 0x1.ffffffffffffep-2, -0x1.fffffffffc51cp-3, |
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| 81 | 0x1.555555557002ep-4, -0x1.a88260c338e75p-30, -0x1.99999f9a7614fp-6, |
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| 82 | 0x1.555e31a1e15e9p-6, -0x1.245240d65e629p-7, -0x1.fa9ba66478903p-11}, |
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| 83 | }; |
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| 84 | |
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| 85 | } // namespace LIBC_NAMESPACE |
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| 86 | |
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